Machine-learning solver for modified diffusion equations

A feedforward neural network has a remarkable property which allows the network itself to be a universal approximator for any function. Here we present a universal machine-learning based solver for multivariable partial differential equations. The algorithm approximates the target functions by neural networks and adjusts the network parameters to approach the desirable solutions. The idea can be easily adopted for dealing with multivariable coupled integrodifferential equations, such as those in the self-consistent field theory for predicting polymer microphase-separated structures.